Category:Path-constrained arcs
From Mintoc
Whenever a path constraint is active, i.e., it holds ![c_i(x(t)) = 0 \; \forall \; t \in [t^\text{start}, t^\text{end}] \subseteq [0, t_f]](/images/math/b/2/a/b2ae1f8d2da30f32c01f209278698096.png)
, and no continuous control 
can be determined to compensate for the changes in 
, naturally 
needs to do so by taking values in the interior of its feasible domain. An illustrating example has been given in [1], where velocity limitations for the energy-optimal operation of New York subway trains are taken into account. The optimal integer solution does only exist in the limit case of infinite switching (Zeno behavior), or when a tolerance is given.
References
- ↑ Sager, S., Reinelt, G., & Bock, H. G. (2009). Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems. Mathematical Programming, 118(1), 109. Bib
Pages in category "Path-constrained arcs"
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